Simplify the following expression: $k = \dfrac{-7a^2 - 7a}{-35a^2 + 14a}$ You can assume $a \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-7a^2 - 7a = - (7 \cdot a \cdot a) - (7 \cdot a)$ The denominator can be factored: $-35a^2 + 14a = - (5\cdot7 \cdot a \cdot a) + (2\cdot7 \cdot a)$ The greatest common factor of all the terms is $7a$ Factoring out $7a$ gives us: $k = \dfrac{(7a)(-a - 1)}{(7a)(-5a + 2)}$ Dividing both the numerator and denominator by $7a$ gives: $k = \dfrac{-a - 1}{-5a + 2}$